Evolution/Taxonomical oddities and mistakes

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It's interesting to see just how subjective and arbitrary most species/subspecies level classifications are in biology. But the species problem is too familiar territory, and I'm hoping to learn if there are any taxonomical issues lying higher up the chain.

Are there any examples of higher level taxonomy designations that tend to break rules, or in some way shirk evolutionary history in their designation? For example, perhaps a "reptile" that actually has an early mammal as an ancestor, and for whatever reason shed those mammalian traits to return to a more "reptilian" mode of existence.

I want to stare at the fine cracks in our biology autism-edifice.